(1)因为 |ab+1| 、|1-b| 均是非负数,它们的和为 0 ,说明它们都等于 0 ,
即 ab+1 = 0 ,1-b = 0 ,
因此解得 a = -1 ,b = 1 .
(2) 1/(ab)+1/[(a+2)(b+2)]+1/[(a+4)(b+4)]+.+1/[(a+2012)(b+2012)]
= 1/(-1*1)+1/(1*3)+1/(3*5)+.+1/(2011*2013)
= -1+1/2*[(1-1/3)+(1/3-1/5)+.+(1/2011-1/2013)]
= -1+1/2*(1-1/2013)
= -1+1006/2013
= -1007/2013 .